Method and apparatus for producing adaptive directional signals

ABSTRACT

The invention relates to adaptive directional systems, and more particularly to a method and apparatus for producing adaptive directional signals. The invention may be applied to the provision of audio frequency adaptive directional microphone systems for devices such as hearing aids and mobile telephones. The method involves constructing the adaptive directional signal ( 46 ) from a weighted sum of a first signal ( 42 A) having an omni-directional polar pattern and a second signal ( 42 B) having a bi-directional polar pattern, wherein the weights are calculated to give the combined signal a constant gain in a predetermined direction and to minimize the power of the combined signal. The method has particular application in producing signals in digital hearing aids, the predetermined direction being in the forward direction with respect to the wearer.

FIELD OF THE INVENTION

The invention relates to adaptive directional systems, and moreparticularly to a method and apparatus for producing adaptivedirectional signals. The invention may be applied to the provision ofaudio frequency adaptive directional microphone systems for devices suchas hearing aids and mobile telephones.

BACKGROUND OF THE INVENTION

In this specification, where a document, act or item of knowledge isreferred to or discussed, this reference or discussion is not anadmission that the document, act or item of knowledge or any combinationthereof was at the priority date:

-   -   (i) part of common general knowledge; or    -   (ii) known to be relevant to an attempt to solve any problem        with which this specification is concerned.

An omni-directional microphone converts sound waves emanating from alldirections into electrical signals to be passed to an output. Adirectional microphone system is typically constructed from two or moreomni-directional microphones, in a configuration that attenuates soundsemanating from certain directions and enhances sounds emanating fromother directions.

The directionality of a particular directional microphone system in thehorizontal plane is represented graphically by a polar pattern, wherethe direction directly in front of the microphone is shown at 0°, andthe direction directly behind the microphone is shown at 180°. The plotof a polar pattern represents gain as a function of the direction ofsound arrival, the gain for any given direction represented by thedistance from the centre of the polar coordinates.

Some of the more common polar patterns are illustrated in FIG. 1, whichshows an omni-directional polar pattern 10 (with no nulls), abi-directional polar pattern 12 (with nulls at 90° and 270°), a cardioidpolar pattern 14 (with a null at 180°) and a super-cardioid polarpattern 16 (with nulls at approximately 135° and 225°)

Directional microphone systems have been employed in the past in hearingaids to improve the signal-to-noise ratio. It is assumed the sound thatthe listener wishes to hear emanates from a forward direction, ie thedirection in front of the listener, and so the directional microphonesystem is designed to provide a maximum gain for sounds emanating fromthis direction whilst attempting to reduce the sounds emanating fromother directions.

Conventionally, directional microphone systems are fixed, meaning thatthe output signal has a fixed polar pattern. Fixed directionalmicrophones traditionally comprise two spaced omni-directionalmicrophones, a delay element and a difference element, and areconfigured to provide a fixed directional signal by subtracting thedelayed signal from the original signal.

Examples of fixed directional microphone systems that do not utilise adelay element are disclosed in U.S. Pat. No. 5,463,694 and U.S. Pat. No.4,712,244. These directional systems instead use a particularcombination of averaging, amplifying, summing, subtracting andintegrating elements that operate on the signals from the microphones toconstruct the fixed directional signal pattern.

As the output from a fixed directional microphone system is a polarpattern with a stationary null, it can only maximally attenuate soundsemanating from a particular direction (although sounds from directionsclose to the null will receive some attenuation). In many practicalsituations this can represent a significant compromise on theperformance of the system. If noise emanates from a direction differentto that of the null, or from multiple directions (which would require acompromise null position), or if there is a moving noise source, areduced signal-to-noise ratio will result.

More complex ‘adaptive’ directional microphone systems have beendeveloped to overcome shortcomings in directional microphone systems.Such systems have the ability to construct varying polar patterns whichare able to dynamically ‘steer’ a null to attenuate signals representingsounds emanating from different directions, or from moving sources.

Known adaptive directional microphone systems are in fact extensions ofconventional fixed systems, and typically utilise a variable delayelement to vary the polar patterns, and thus provide adaptivedirectional signals. The architecture of such an adaptive directionalmicrophone system is illustrated in FIG. 2. Front 20 and rear 22omni-directional microphones transduce sound waves into front 21 andrear 23 electrical signals.

When a sound wave arrives from the forward direction, it reaches thefront microphone first, and hence the rear signal 23 is a delayedversion of the front signal 21. Likewise, if the sound arrives frombehind, the front signal 21 is a delayed version of the rear signal 23.If the sound arrives from the side, there is no delay between the twosignals 21 and 23. In short, the delay between the two signals isdependent on the angle of arrival of the sound wave. A variable delayelement 24, coupled to the rear microphone 22, is used to match thedelay corresponding to the desired cancellation direction. This producesa delayed rear signal 25. This signal 25 is received by a differenceelement 26 also coupled to the front microphone 20, configured as shownto output the difference between signals 21 and 25 to produce thedirectional output signal 30. As will be understood by those skilled inthe art, the adaptive nature of this system is provided by a feedbackloop, the adaptive directional signal 30 feeding back to an optimisingalgorithm element 28, which in turn provides an optimised delay value 29to the variable delay element 24 used in producing delayed rear signal25. The system is therefore designed to iteratively converge to adesired solution, in accordance with the algorithm implemented byelement 28.

Various examples of known adaptive directional microphone systems thatuse variable delay elements are described in U.S. Pat. No. 5,757,933,US-2001/0028720, US-2001/0028718, U.S. Pat. No. 6,539,096 and U.S. Pat.No. 6,339,647. The main disadvantages of these systems are thecomplexity involved in implementing the variable delay element, alongwith the possible instability introduced through the use of a feedbackstructure.

Adaptive directional microphone systems that do not employ variabledelay elements are also known, and examples of such systems aredescribed in WO-01/97558 and US-2003/0031328. Both systems utilise twofixed delay elements to generate a forward-facing and a backward-facingcardioid polar pattern, which respectively represent an ‘enhancedsignal’ and an ‘enhanced noise’. The enhanced noise and enhanced signalare then combined to produce an adaptive directional signal. Anoptimisation algorithm is used to find the ideal combination of the twosignals to give maximum noise rejection. A major disadvantage of theseadaptive directional systems is again their reliance on delay elements,in this case multiple fixed delay elements. As discussed above, theseelements can be very difficult to implement in hardware, or require aspecially designed allpass filter, which significantly increases theprocessing requirements of the system, particularly when implementedusing a digital signal processor.

Adaptive directional microphone systems have also been developed that,instead of being continuously variable, simply select an output from arange of signals that have been implemented. One of the simplestapproaches is described in U.S. Pat. No. 6,327,370, and involves using afixed directional signal and an omni-directional signal, with aselection between the signals based on prescribed criteria such asambient noise level. The idea has been extended in the teaching of U.S.Pat. No. 6,522,756, which includes a greater number of directionalsignals for selection. Such ‘signal selection’ systems are quite simpleand can perform well, however for adequate performance they require manysignals to be generated simultaneously, greatly increasing the demandson hardware and processing power. In addition, the limited choice ofbeam types signifies a discontinuous response, such that a signal withan optimum polar pattern cannot always be found.

There remains a need to provide an improved, or at least an alternative,method and apparatus for producing adaptive directional signals.

SUMMARY OF THE INVENTION

According to one form of the invention a method for producing anadaptive directional signal is provided, the method includingconstructing the adaptive directional signal from a weighted sum of afirst signal having an omni-directional polar pattern and a secondsignal having a bi-directional polar pattern, wherein the weights arecalculated to give the combined signal a constant gain in apredetermined direction and to minimise the power of the combinedsignal.

By minimising the power of the constructed adaptive directional signal,the amplitude of signals received from directions other than thepredetermined direction is minimised.

The directional signal is produced by the optimised weights that ineffect, adaptively vary the relative contributions of the first andsecond signals, to thereby minimise or eliminate the contribution ofsignals emanating from directions other than the predetermineddirection. Thus it will be realised that the polar pattern of thecombined signal will vary in response to changes in the first and secondsignals, whilst providing a constant gain for signals that emanate fromthe predetermined direction. For example, the adaptive directionalsignal may have a cardioid, super-cardioid, or even an omni-directionalpolar pattern, depending on the calculated weightings.

In a preferred embodiment, the first and second signals are derived fromsignals produced by two spaced omni-directional microphones, a front anda rear microphone, and said predetermined direction is the forwarddirection along the microphone axis. The method of the present inventionis also applicable to signals produced from an array of more than twomicrophones.

Preferably, the second signal is provided by the difference betweensignals produced by two spaced omni-directional microphones, without theuse of a delay element.

In accordance with this embodiment, the method may further includeprocessing the second signal by means of an integrator element or anintegrator-like filter before constructing the combined signal, therebycompensating for the attenuation of low frequencies and phase shiftsintroduced in the subtraction of the two omni-directional signals.

Preferably, the microphones are matched, which can be accomplished byusing physically matched microphones or by employing a gain element tomatch the microphone outputs.

A weight may be calculated in any convenient manner that provides forthe constant gain of the combined polar pattern in the forward directionand minimises the power of the combined signal. Typically the constantgain is provided by imposing a consent that the first signal weight andthe second signal weight add to one.

In preferred embodiments the weights are calculated in a non-iterativemanner, such as by solving the following equation:

$a = \frac{{\sum y^{2}} - {\sum{xy}}}{{\sum x^{2}} - {2{\sum{xy}}} + {\sum y^{2}}}$Where:

-   -   a=weight for the first signal    -   (1−a)=weight for the second signal    -   x=first signal sample    -   y=second signal sample.

A weight may be calculated for a frame of predetermined lengthconsisting of N first signal samples and N second signal samples. Thelength of the frame (N) generally depends upon the environment ofapplication of the method, however a suitable frame length for audiofrequency signals is 32 or 64 samples long. The weighting factor maychange significantly from frame to frame, so the series of weight valuesmay also be filtered or smoothed to minimise frame to frame variation inthe weight (which may otherwise be heard as audible artifacts).

In another embodiment weights are calculated continuously for each firstsignal sample and second signal sample. This is achieved by calculatingx², y² and xy for each sample and adding them to the appropriate runningsum. A leaky integrator (an integrator having a feedback coefficientslightly less than one) can be used to perform the running sum in orderto prevent overflows and to ensure that the system's ‘memory’ is not toolong. This embodiment allows a new weighting factor to be calculatedevery time that a new sample is available, rather than having to waitfor a whole frame of samples.

In another embodiment, the first and second signals (ie the variables xand y in the form described above) can be frequency domain samplesrather than time domain samples. In this case the optimisation of theweighting factor (a) can be calculated as above, but with the addedadvantage that the weighting factor can be calculated and applied toseveral independent subsets of frequency domain samples (givingdifferent directional responses at different frequencies). Also, if somefrequencies are deemed to be more important to suppress than others,they can be given a higher weighting before calculating the weightingfactor (a). This allows the system to focus on rejecting only (say)speech-type sounds, or machinery sounds. A similar approach can beapplied in the time domain through the use of time domain filters.

The sums used for calculating the weighting factor a can also be used todetect particular conditions that require a different signal processingapproach. For example, if Σx² is particularly small, then theenvironment is quiet, which suggests that an omni-directional responseis more suitable than a directional response. In this case a simplethreshold test could be performed to decide on the appropriate strategy.

The invention is based on the realisation that an adaptive directionalsignal of varying polar pattern can be constructed from a weighted sumof an omni-directional and a bi-directional polar pattern which can beeasily generated without the use of delay elements. Surprisingly,despite the simplicity of the system of the invention, theoreticalanalysis and test results have demonstrated extremely good performancein terms of noise reduction and signal enhancement.

According to a further form of the invention, an apparatus for producingan adaptive directional signal is provided, the apparatus including:

-   -   means for producing a first signal having an omni-directional        polar pattern and a second signal having a bi-directional polar        pattern; and    -   means for constructing the adaptive directional signal from a        weighted sum of the first and second signals, wherein the        weights are calculated to give the combined signal a constant        gain in a predetermined direction and to minimise the power of        the constructed adaptive directional signal.

The apparatus preferably includes means to provide said constant gain byimposing a constraint that the first signal weight and the second signalweight add to a predetermined value.

In a preferred form, the apparatus includes means for calculating theweights by solving the following equation:

$a = \frac{{\sum y^{2}} - {\sum{xy}}}{{\sum x^{2}} - {2{\sum{xy}}} + {\sum y^{2}}}$where:

-   -   a=weight for the first signal    -   (1−a)=weight for the second signal    -   x=first signal sample    -   y=second signal sample.

The apparatus may include means for calculating said signal weights fora series of frames, each frame having a predetermined length consistingof N first signal samples and N second signal samples.

A filter for filtering or smoothing the series of weights may beincluded, to minimise frame-to-frame variation in the calculatedweights.

The apparatus may include means for calculating said weightscontinuously for samples of said first and second signals. Further, itmay include a leaky integrator to perform a running sum on said firstand second signal samples in order to address issues of numericaloverflow in the system memory.

Means may be included for calculating said weights so as to construct anomnidirectional combined signal when the total power in said firstsignal is below a certain value.

In a preferred form the apparatus may include two spaced omnidirectionalmicrophones, a front and a rear microphone, signals from which are usedfor deriving said first and second signals, and said predetermineddirection is the forward direction along the microphone axis. Further,means may be included for providing said second signal from thedifference between signals produced by the front and rear microphones,without the use of a delay element.

The apparatus may include an integrator element or an integrator-likefilter for processing the second signal before constructing the combinedsignal, thereby compensating for the attenuation of low frequencies andphase shifts introduced in the provision of the second signal.

Further, the apparatus may include means for amplifying the signalsproduced by the front and/or the rear microphone before the step ofconstructing the bi-directional signal, to ensure an equivalent gainbetween the microphones.

The invention thus serves to provide a directional response thatadaptively provides the desired performance, by fixing the gain in theforward direction, while minimising the power received.

Importantly, and in contrast with the prior art, the invention avoidsthe need to use delay elements in providing the adaptive directionalresponse. Instead of an iterative approach converging on a desiredsolution, the method of the present invention mathematically calculatesthe required weights to apply to combining the signal patterns inaccordance with the preset constraints on a frame-by-frame orsample-by-sample basis.

The invention can also be applied to sub-band processing, providing adifferent adaptive response in different frequency bands.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be further explained and illustrated by way of anon-limiting example and with reference to the accompanying drawings, inwhich:

FIG. 1 is an illustration of the polar patterns of various directionalsignals;

FIG. 2 is a schematic drawing of an adaptive directional microphonesystem of the prior art;

FIG. 3 is a schematic drawing of an apparatus for producing an adaptivedirectional signal in accordance with an embodiment of the presentinvention;

FIG. 4 is a flow chart representing a method for producing an adaptivedirectional signal in accordance with an embodiment of the presentinvention; and

FIG. 5 illustrates two example adaptive directional signals produced byimplementing the method of the present invention.

Turning to FIG. 3, the architecture of an apparatus for producing anadaptive directional signal is illustrated. The same reference numeralsas those used in FIG. 2 are employed to reference similar components.The apparatus is configured as explained below to combine the output ofmultiple microphones to produce an adaptively directional output. Front20 and rear 22 omni-directional microphones respectively transduce soundwaves into front 21 and rear 23 signals. Microphones 20 and 22 should bematched, and this can be accomplished either by using physically matchedmicrophones or by employing a gain element (shown at 35 in FIG. 3) toselectively match the microphone outputs. The front 20 and rear 22microphones also include suitable analogue-to-digital converters (notshown) for providing the front 21 and rear signals 22 in a digital form.

As noted above, the delay between the front signal and the rear signalwill depend on the angle from which the incident sound arrives. Frontsignal 21 and rear signal 23 are passed to a differencing element 26 forsubtraction of rear signal 23 from front signal 21 to produce a signal34 with a bi-directional polar pattern. This bipolar signal 34attenuates sounds emanating from directions perpendicular to the axis ofthe front 20 and rear 22 microphones, whilst front signal 21 retains anomni-directional polar pattern.

Because the bi-directional signal 34 is generated by the differencebetween two delayed samples it inherently introduces a differentiated(high pass) frequency response that tends to produce undesirableattenuation of lower frequencies and a phase shift at all frequencies.To counter this effect, the bi-directional signal 34 is passed to anintegrator 32 in order to give the signal 34 a flat frequency responseand at the same time to automatically correct for the phase shift thatis introduced during construction of the bi-directional signal. Thisintegrator can also be replaced by a filter with a similar response tothe integrator. This allows other undesirable artifacts (such as a dcoffset) to be removed from the bi-directional signal.

The integrated signal 36 and the front microphone (omni-directional)signal 21 are directed to an optimiser 38 that calculates respectivefront signal weights 39A and rear signal weight 39B by means of anoptimising algorithm described in further detail below.

The optimiser 38 calculates weights 39A and 39B subject to theconstraint that the directional response of the system has a constantgain in the forward direction. Where the signals are of audio frequencyand the system is employed in a hearing aid, this direction willgenerally be selected as the forward direction, ie, along the axis ofthe front 20 and rear 22 microphones. This is in accordance with theassumption noted above that the listener wishes to hear sounds emanatingfrom the forward direction.

The constant gain in the forward directional is achieved by constrainingthe weights 39A and 39B to add to 1.0. This prevents sound emanatingfrom the forward direction being attenuated in the adaptive directionalsignal produced by the apparatus.

It should be realised however, that the weights can be calculated togive a constant gain to signals emanating from a selected otherdirection, which may be useful in other applications or in accordancewith other microphone configurations.

The optimisation algorithm is configured to calculate weights 39A and39B to minimise the signal power produced. By minimising the power ofthe signal, the noise component (defined as signals from any directionother than the front) is minimised, thereby providing an improvedsignal-to-noise ratio.

The weights 39A and 39B calculated by the optimiser 38 in accordancewith the optimisation algorithm are applied to respective variable gainelements 40A and 40B to which front signal 21 and bi-directional signal36 are passed. The variable gain elements thus apply weighted gains tothe samples that comprise signals 21 and 36, to produce respectiveweighted signals 42A and 42B.

The weighted signals 42A and 42B are then passed to a summing element 44that outputs an adaptive directional signal 46 by summing the weightedsignals 42A and 42B. The adaptive directional signal 46 is thenprocessed further (if required) and then output to suitable outputmeans, such as an earphone speaker (not shown).

Turning to FIG. 4, the steps carried out by the optimiser in calculatingthe weights are illustrated with reference to a flow chart. In use, theoptimiser is a suitable digital signal processing apparatus, as would beunderstood by those skilled in the art. At steps 50 and 52 the optimiserreceives a sampled value of the omnidirectional signal and thebi-directional signal. In this embodiment, the weights are calculated ona frame by frame basis, with each frame being 64 samples long.Therefore, at step 56 a test is performed of whether the end of theframe has been reached. If the test is negative, step 54 is carried outand the value of the omni-directional sample and bi-directional sampleare accumulated in the following summations:

-   -   Σx²    -   Σy² and    -   Σxy        where x=the omni-directional sample series; and    -   y=the bi-directional sample series.

If the test is positive, the weight for the omni-directional signal a iscalculated at step 58 using the accumulated sums in the followingformula:

$a = \frac{{\sum y^{2}} - {\sum{xy}}}{{\sum x^{2}} - {2{\sum{xy}}} + {\sum y^{2}}}$

As noted above, the weight is optimised subject to the constraint thatthere is to be a constant gain in the forward direction, which isimposed by setting the sum of the omni-directional and bi-directionalweights equal to one. From this, the bi-directional weight is simplycalculated as (1−a). Also, as noted previously, other criteria can beapplied in calculating a, such as forcing it to 1 (i.e. anomni-directional response) when in a quiet environment (if Σx² issmall).

The derivation of the above formula is found by using the constraintthat the total power of the output adaptive directional signal is to beminimised. Therefore:Energy=Σ(ax(t)+(1−a)y(t))²

Differentiating with respect to a to find the point of minimum energygives:

$\begin{matrix}{\frac{\mathbb{d}{Energy}}{\mathbb{d}a} = 0} \\{= {{2a\left( {{\sum x^{2}} - {2{\sum{xy}}} + {\sum y^{2}}} \right)} +}} \\{2\left( {{\sum{xy}} - {\sum y^{2}}} \right)}\end{matrix}$

Solving for a gives:

$a = \frac{{\sum y^{2}} - {\sum{xy}}}{{\sum x^{2}} - {2{\sum{xy}}} + {\sum y^{2}}}$

Returning to the flow chart at step 60, the calculated weights arefiltered to guard against excessive frame to frame variation in theweights.

In an alternative embodiment, the values Σx², Σy² and xy are filteredprior to the calculation of the weights. This can be particularly usefulwhen processing samples continuously and can be implemented efficientlyif the summing operations used in the calculations of the weights areimplemented as ‘leaky integrators’ (ie an integrator with a feedbackcoefficient slightly less than one). This allows a new weighting factorto be calculated every time a new sample is available, rather thanhaving to wait for a whole frame of samples.

The final step 62 in the process illustrated is the outputting of theweights 42A and 42B.

In a further alternative embodiment the weights may be calculated overmultiple frames, or continuously.

Turning to FIG. 5, the effect of different omni-directional andbi-directional weights on the polar pattern of the output adaptivedirectional signal produced (under the constraints defined above) isillustrated. The directional signal (46 and 46′ in FIG. 5) isconstructed from the weighted contributions of the omni-directional42A/42A′ and bi-directional signals 42B/42B′.

For example, an omni-directional weight of 0.5 and a bi-directionalweight of 0.5 produce a directional signal 46 having a cardioid polarpattern as shown. The equal weighting used means that the rear lobe ofthe bi-directional signal exactly cancels with the omni-directionalsignal in that direction.

In the second example in FIG. 5, the omni-directional signal 42A′ andbi-directional signal 42B′ are given weights of 0.375 and 0.625respectively, providing a directional signal having a super-cardioidpolar pattern as illustrated.

It should also be noted that in certain situations, due to theconstraints imposed in accordance with the invention, an adaptivedirectional signal having an omni-directional polar pattern may beproduced, ie when an omni-directional weight of 1 (and thus abi-directional weight of 0) is applied. This can be the result, forexample, in quiet conditions or in conditions with high levels of windnoise. In such situations the omni-directional pattern is desirable, andin contrast with prior art systems (which require to be configured toswitch to an omni-directional pattern under prescribed conditions), theinvention allows the system to automatically adopt such a response.

Adaptive Directional Microphone Results

The adaptive directional microphone of the present invention wasimplemented in a behind-the-ear hearing aid and the speech perception ofeight listeners with impaired hearing was evaluated against anomnidirectional microphone and a fixed supercardioid directionalmicrophone. The speech test used was the Hearing In Noise Test (HINT) inwhich a speech shaped noise is presented together with spoken sentences,and the level of the noise is adjusted until the listener recognizes 50%of the sentences correctly.

The HINT scores are expressed as signal-to-noise ratio (SNR) at thepoint where the listener is scoring 50% correct.

The listeners were fitted with two hearing aids, binaurally. The speechwas presented from a speaker in front of the listener, and the noise waspresented at three different angles (90, 135, and 180 degrees from thefront), on one side only. The mean HINT scores for the eight listeners,averaged across angles were −0.38 dB for the omnidirectional microphone,−4.09 dB for the supercardioid fixed directional microphone, and −5.18dB for the adaptive directional microphone of the present invention.

Negative SNR values indicate that the noise is louder than the speech,and hence that the adaptive directional microphone system of the presentinvention is allowing the listener to cope with a greater noise level.

The adaptive directional microphone performed significantly better onthis test than either the omnidirectional or the supercardioid fixeddirectional microphone.

Microphone Angle for noise HINT SNR in dB adaptive 135° −5.12 adaptive180° −4.63 adaptive  90° −5.78 supercardioid 135° −4.54

Microphone Angle for noise HINT SNR in dB supercardioid 180° −2.76supercardioid  90° −4.96 omnidirectional 135° −0.42 omnidirectional 180°2.72 omnidirectional  90° −1.16

The invention can be implemented in hardware or software, and in theapplication to a hearing aid is preferably implemented in a DSP chip,with samples from the signals produced by each microphone used tocalculate the fixed polar patterns employed as inputs to the adaptivedirectionality process.

Modifications and improvements to the invention will be readily apparentto those skilled in the art. Such modifications and improvements areintended to be within the scope of this invention. For example, whilstthe above has been described by reference to the time domain, theteachings of the present invention apply equally in the frequencydomain.

1. A method executed by a processor for producing a combined adaptivedirectional signal, the method comprising: constructing the combinedadaptive directional signal from a weighted sum of a first signal weightof a first sound signal having an omni-directional polar pattern and asecond signal weight of a second sound signal having a bi-directionalpolar pattern wherein the first signal weight and the second signalweights are calculated to give the combined signal a constant gain in apredetermined direction and to minimize power of the combined signal,wherein the weights are calculated by the processor in a non-iterativemanner, and wherein the signal weights are calculated by solving thefollowing equation:$a = \frac{{\sum y^{2}} - {\sum{xy}}}{{\sum x^{2}} - {2{\sum{xy}}} + {\sum y^{2}}}$where a=weight for the first signal (1−a)=weight for the second signalx=first signal sample y=second signal sample.
 2. A method according toclaim 1, wherein the first and second signals are sampled, the signalweights being calculated for successive sets of said first and secondsignals samples.
 3. A method according to claim 1, wherein the first andsecond signals are sampled, the signal weights being calculated forsuccessive sets of said first and second signals samples, and the signalweights are calculated continuously by calculating x², y², and xy foreach sample and adding them to an appropriate running sum.
 4. A methodaccording to claim 3, wherein a leaky integrator is used to perform therunning sum in order to address issues of numerical overflow.
 5. Amethod in accordance with claim 1, wherein the second signal having abi-directional polar pattern is derived from a first omni-directionalmicrophone and from a second omni-directional microphone, and whereinthe first signal having an omni-directional polar pattern is derivedfrom one of the first and second omni-directional microphones.
 6. Amethod according to claim 1, wherein said signal weights are calculatedso as to construct an omni-directional combined signal when a totalpower in said first signal is below a certain value and value a defaultsto a value of 1.0 in the event that Σx² is less than a prescribedminimum value.
 7. A method according to claim 5, wherein theomni-directional microphones comprise a front microphone and a rearmicrophone, and said predetermined direction is the forward directionalong the microphone axis.
 8. A method according to claim 7, wherein thesecond signal is provided by the difference between signals produced bythe front and rear microphones, without the use of a delay element.
 9. Amethod according to claim 8, further comprising processing the secondsignal by means of an integrator element or an integrator-like filterbefore constructing the combined signal, thereby compensating for theattenuation of low frequencies and phase shifts introduced in thesubtraction of the two omni-directional signals.
 10. A method accordingto claim 8, further comprising amplifying the signals produced by one ormore of the front and the rear microphone before constructing thebi-directional signal, to ensure an equivalent gain between themicrophones.
 11. A method according to claim 1, wherein said first andsecond signals are frequency domain samples.
 12. A method according toclaim 11, further comprising calculating and applying the weights toseveral independent subsets of frequency domain samples, to givedifferent directional responses at different frequencies and/or to allowselective suppression of different frequencies.
 13. A method accordingto claim 1, comprising applying a frequency weighting function to saidfirst and second signal before calculating said signal weights.
 14. Anapparatus for producing a combined adaptive directional signal, theapparatus comprising: an analog-to-digital converter for producing afirst sound signal having an omni-directional polar pattern and, asecond sound signal having a bi-directional polar pattern; a summationdevice for constructing the adaptive directional signal from a weightedsum of a first signal weight of the first signal and a second signalweight of the second signal, wherein the first signal weight and thesecond signal weight are calculated to give the combined signal aconstant gain in a predetermined direction and to minimize power of thecombined signal; and means for calculating the weights by solving thefollowing equation:$a = \frac{{\sum y^{2}} - {\sum{xy}}}{{\sum x^{2}} - {2{\sum{xy}}} + {\sum y^{2}}}$where: a=weight for the first signal (1−a)=weight for the second signalx=first signal sample y=second signal sample.
 15. An apparatus accordingto claim 14, further comprising a first omni-directional microphone anda second omni-directional microphone, wherein the second signal having abi-directional polar pattern is derived from the first and secondomni-directional microphones and wherein the first signal having anomni-directional polar pattern is derived from one of the first andsecond omni-directional microphones.
 16. An apparatus according to claim14, including means for calculating said signal weights for a series offrames, each frame having a predetermined length consisting of N firstsignal samples and N second signal samples.
 17. An apparatus accordingto claim 14, including a filter for filtering or smoothing the series ofweights to minimize frame-to-frame variation in the calculated weights.18. An apparatus according to claim 14, including means for calculatingsaid weights continuously for samples of said first and second signals.19. An apparatus according to claim 14, further comprising leakyintegrator to perform a running sum on said first and second signalsamples in order to address issues of numerical overflow system memory.20. An apparatus according to claim 14, further comprising means forcalculating said signal weights so as to construct an omni-directionalcombined signal when a total power in said first signal is below acertain value.
 21. An apparatus according to claim 15, wherein the twoomni-directional microphones comprise a front microphone and a rearmicrophone, and wherein said predetermined direction is the forwarddirection along an axis of the microphones.
 22. An apparatus accordingto claim 21, further comprising means for providing said second signalfrom the difference between signals produced by the front and rearmicrophones, without the use of a delay element.
 23. An apparatusaccording to claim 21, further comprising integrator element or anintegrator-like filter for processing the second signal beforeconstructing the combined signal, thereby compensating for attenuationof low frequencies and phase shifts introduced in the provision of thesecond signal.
 24. An apparatus according to claim 21, furthercomprising means for amplifying the signals produced by the front and/orthe rear microphone before the step of constructing the bi-directionalsignal, to ensure an equivalent gain between the microphones.
 25. Amethod according to claim 1, wherein said signal weights are calculatedfor a series of frames, each frame having a predetermined lengthcomprising of N first signal samples and N second signal samples.
 26. Amethod according to claim 25, wherein N=64.
 27. A method according toclaim 25, further including filtering or smoothing the series of weightsto minimise frame-to-frame variation in the calculated weights.